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\usepackage{amsmath, amssymb} % 数学公式与符号
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\title{《基础复分析》第1章复数 - 编程实验}
\author{AI ET AL}

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\begin{document}
\maketitle 

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\section*{实验一：复数的基本运算}

\textbf{实验目的：} 编程验证复数的基本运算性质，包括根的计算和模长性质。

\textbf{实验内容：} 基于习题1, 4, 5，验证复数运算的基本性质。

\textbf{实验任务：}
\begin{enumerate}[left=4em]
    \item 运行代码，验证各种根的计算
    \item 验证复数模长的性质
\end{enumerate}

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\section*{实验二：复数方程求解}

\textbf{实验目的：} 使用Python求解复数方程，计算单位根。

\textbf{实验内容：} 基于习题2, 10, 16, 17，实现复数方程求解和单位根计算。

\textbf{实验任务：}
\begin{enumerate}[left=4em]
    \item 运行代码，验证复数二次方程的求解
    \item 计算不同次数的单位根
\end{enumerate}

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\section*{实验三：复数的几何应用}

\textbf{实验目的：} 使用Python验证复数在几何中的应用。

\textbf{实验内容：} 基于习题8, 9, 11, 12, 18，实现复数的几何性质验证。

\textbf{实验任务：}
\begin{enumerate}[left=4em]
    \item 运行代码，验证椭圆上点的性质
    \item 验证不同几何图形的性质
\end{enumerate}

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\section*{实验总结}
通过这三个编程实验，我们：
\begin{itemize}
    \item 验证了复数的基本运算性质
    \item 实现了复数方程的求解和单位根计算
    \item 应用复数验证了几何性质
\end{itemize}

\end{document}

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